Question

Defining the Tangent space to the boundary of a manifold $T_p(\partial S)$

score 37 · Answer 1 · 2026-03-26 17:53:44

37

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Defining the Tangent space to the boundary of a manifold $T_p(\partial S)$

Published on 26 Mar 2026 - 17:53

score 62 · Answer 2 · 2026-03-22 07:04:58

62

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Is a $C^p$ ($p \geq 1$) orientable closed $(k-1)$-manifold always the boundary of a $C^p$ $k$-manifold-with-boundary in $\mathbb{R}^n$?

Published on 22 Mar 2026 - 7:04

score 54 · Answer 3 · 2026-03-22 13:30:57

54

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A prime orientable 3-manifold containing a nonseparating 2-sphere is homeomorphic to $S^2\times S^1 $.

Published on 22 Mar 2026 - 13:30

score 87 · Answer 4 · 2026-03-22 05:46:59

87

Views

Why can we replace the euclidean space with the upper half space as model space for a manifold

Published on 22 Mar 2026 - 5:46

score 47 · Answer 5 · 2026-03-22 14:22:30

47

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Names of two manifold-like structures

Published on 22 Mar 2026 - 14:22

score 36 · Answer 6 · 2026-03-25 11:16:31

36

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Disjoint curves connecting specified pairs of points on the edge of a Möbius strip

Published on 25 Mar 2026 - 11:16

score 51 · Answer 7 · 2026-03-22 05:12:48

51

Views

Guillemin's proof of manifold boundary dimension

Published on 22 Mar 2026 - 5:12

score 52 · Answer 8 · 2026-03-22 11:07:09

52

Views

Does collar restrict to a closed neighbourhood?

Published on 22 Mar 2026 - 11:07

score 54 · Answer 9 · 2026-03-26 09:39:49

54

Views

Whether $\mathbb{T}\times [0,1]$ is diffeomorphic to $\mathbb{D}^2$?

Published on 26 Mar 2026 - 9:39

score 590 · Answer 10 · 2026-03-22 15:15:15

590

Views

Invertibility theorem on the boundary for a function between two closed 2D manifolds

Published on 22 Mar 2026 - 15:15

score 112 · Answer 11 · 2026-03-21 21:09:13

112

Views

$G$ is an $(n-1)$-manifold without boundary and is the topological boundary to an open $K\subset \mathbb{R}^n$. Prove $G \cup K$ is an $n$-manifold.

Published on 21 Mar 2026 - 21:09

score 287 · Answer 12 · 2026-03-22 03:00:49

287

Views

Differential-form version of Cauchy-Schwarz on manifold boundary

Published on 22 Mar 2026 - 3:00

score 185 · Answer 13 · 2026-03-22 10:03:55

185

Views

maximum principle on compact manifolds with boundary

Published on 22 Mar 2026 - 10:03

score 4.4k · Answer 14 · 2026-03-21 18:57:45

4.4k

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What does it mean for a manifold to be oriented?

Published on 21 Mar 2026 - 18:57

score 61 · Answer 15 · 2026-03-22 00:23:24

61

Views

Smooth mapping between manifold such that $\text{Im}(f) \subset \partial N$

Published on 22 Mar 2026 - 0:23

List Question

Defining the Tangent space to the boundary of a manifold $T_p(\partial S)$

Is a $C^p$ ($p \geq 1$) orientable closed $(k-1)$-manifold always the boundary of a $C^p$ $k$-manifold-with-boundary in $\mathbb{R}^n$?

A prime orientable 3-manifold containing a nonseparating 2-sphere is homeomorphic to $S^2\times S^1 $.

Why can we replace the euclidean space with the upper half space as model space for a manifold

Names of two manifold-like structures

Disjoint curves connecting specified pairs of points on the edge of a Möbius strip

Guillemin's proof of manifold boundary dimension

Does collar restrict to a closed neighbourhood?

Whether $\mathbb{T}\times [0,1]$ is diffeomorphic to $\mathbb{D}^2$?

Invertibility theorem on the boundary for a function between two closed 2D manifolds

$G$ is an $(n-1)$-manifold without boundary and is the topological boundary to an open $K\subset \mathbb{R}^n$. Prove $G \cup K$ is an $n$-manifold.

Differential-form version of Cauchy-Schwarz on manifold boundary

maximum principle on compact manifolds with boundary

What does it mean for a manifold to be oriented?

Smooth mapping between manifold such that $\text{Im}(f) \subset \partial N$

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